VFD approach to the computation TE and TM modes in elliptic waveguide on TM grid

We describe here a vector finite difference approach (VFD) to the evaluation of eigenvalues and modes of elliptical wave guides. The FD is applied using a 2D elliptical grid in the waveguide section. A suitable Taylor expansion of the vector mode function allows to take exactly into account the boundary condition. To prevent the raising of spurious modes, our FD approximation results in a constrained eigenvalue problem, that we solve using a decomposition method. This approach has been evaluated comparing our results to known data for the elliptic case.